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Mat. Zametki, 1976, Volume 19, Issue 5, Pages 795–804 (Mi mz7800)  

This article is cited in 1 scientific paper (total in 1 paper)

An extremal theorem of Riemannian geometry

S. V. Buyalo

Leningrad State University

Abstract: An exact upper estimate for the volume of a tubular neighborhood of a smooth submanifold $N$ of a complete Riemann space $M$ depending upon the volume of $N$ and lower bound for the sectional curvatures of $M$ is given. If $N$ is a closed geodesic, then the equality is attained in the estimate if and only if $M$ is a generalized lens space.

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English version:
Mathematical Notes, 1976, 19:5, 468–473

Bibliographic databases:

UDC: 513.8
Received: 31.03.1975

Citation: S. V. Buyalo, “An extremal theorem of Riemannian geometry”, Mat. Zametki, 19:5 (1976), 795–804; Math. Notes, 19:5 (1976), 468–473

Citation in format AMSBIB
\Bibitem{Buy76}
\by S.~V.~Buyalo
\paper An extremal theorem of Riemannian geometry
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 5
\pages 795--804
\mathnet{http://mi.mathnet.ru/mz7800}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=425840}
\zmath{https://zbmath.org/?q=an:0337.53042|0332.53024}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 5
\pages 468--473
\crossref{https://doi.org/10.1007/BF01142573}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. D. Burago, V. A. Zalgaller, “Convex sets in Riemannian spaces of non-negative curvature”, Russian Math. Surveys, 32:3 (1977), 1–57  mathnet  crossref  mathscinet  zmath
  • Математические заметки Mathematical Notes
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